problem here is that he would likely shove most of the turn cards, so you can´t really count that he´d check turn and you also see river card
So i prefer folding or if you think he is capable bluffing or raising there with draws then shoving that you see turn and river card and also get to showdown
Since board is not that drawy you can always c-bet less to 4.5$ which would likely work the same as 5.75$